/ - черта дроби
(x-6)/(x+1) + (2+x)/(x-1) = 6/(x^2 - 1)
(x-1)(x-6)/(x^2 - 1) + (2+x)(x+1)/(x^2 - 1) = 6/(x^2 - 1)
(x-1)(x-6) + (2+x)(x+1) - 6 = 0
x^2 - 7x + 6 + 2x + 2 + x^2 + x - 6 = 0
2x^2 - 4x + 2 = 0 | : 2 (делим все на 2)
x^2 - 2x + 1 = 0
a = 1, b = -2, c = 1
D = b^2 - 4ac = 4 - 4 = 0
x = -b/2a = 2/2 = 1
ответ: x = 1
/ - черта дроби
(x-6)/(x+1) + (2+x)/(x-1) = 6/(x^2 - 1)
(x-1)(x-6)/(x^2 - 1) + (2+x)(x+1)/(x^2 - 1) = 6/(x^2 - 1)
(x-1)(x-6) + (2+x)(x+1) - 6 = 0
x^2 - 7x + 6 + 2x + 2 + x^2 + x - 6 = 0
2x^2 - 4x + 2 = 0 | : 2 (делим все на 2)
x^2 - 2x + 1 = 0
a = 1, b = -2, c = 1
D = b^2 - 4ac = 4 - 4 = 0
x = -b/2a = 2/2 = 1
ответ: x = 1